Wilson primes of order n: Difference between revisions
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Line 28:
# ( ( n - 1 )! x ( p - n )! - (-1)^n ) mod p^2 = 0 #
PR read "primes.incl.a68" PR # include prime utilities #
[]BOOL primes = PRIMESIEVE 11
# returns TRUE if p is an nth order Wilson prime #
PROC is wilson = ( INT n, p )BOOL:
Line 50:
IF is wilson( n, 2 ) THEN print( ( " 2" ) ) FI;
FOR p FROM 3 BY 2 TO UPB primes DO
IF
IF is wilson( n, p ) THEN print( ( " ", whole( p, 0 ) ) ) FI
FI
OD;
print( ( newline ) )
Line 507 ⟶ 509:
11 | 17 2713
</pre>
=={{header|EasyLang}}==
{{trans|FreeBASIC}}
<syntaxhighlight>
func isprim num .
i = 2
while i <= sqrt num
if num mod i = 0
return 0
.
i += 1
.
return 1
.
func is_wilson n p .
if p < n
return 0
.
prod = 1
p2 = p * p
for i = 1 to n - 1
prod = prod * i mod p2
.
for i = 1 to p - n
prod = prod * i mod p2
.
prod = (p2 + prod - pow -1 n) mod p2
if prod = 0
return 1
.
return 0
.
print "n: Wilson primes"
print "-----------------"
for n = 1 to 11
write n & " "
for p = 3 step 2 to 10099
if isprim p = 1 and is_wilson n p = 1
write p & " "
.
.
print ""
.
</syntaxhighlight>
=={{header|F_Sharp|F#}}==
Line 726 ⟶ 773:
3010 PROD# = PROD# - INT(PROD#/P2)*P2
3020 RETURN</syntaxhighlight>
=={{header|J}}==
<syntaxhighlight lang="j"> wilson=. 0 = (*:@] | _1&^@[ -~ -~ *&! <:@[)^:<:
(>: i. 11x) ([ ;"0 wilson"0/ <@# ]) i.&.(p:inv) 11000
┌──┬───────────────┐
│1 │5 13 563 │
├──┼───────────────┤
│2 │2 3 11 107 4931│
├──┼───────────────┤
│3 │7 │
├──┼───────────────┤
│4 │10429 │
├──┼───────────────┤
│5 │5 7 47 │
├──┼───────────────┤
│6 │11 │
├──┼───────────────┤
│7 │17 │
├──┼───────────────┤
│8 │ │
├──┼───────────────┤
│9 │541 │
├──┼───────────────┤
│10│11 1109 │
├──┼───────────────┤
│11│17 2713 │
└──┴───────────────┘</syntaxhighlight>
=={{header|Java}}==
Line 952 ⟶ 1,027:
10: 11 1109
11: 17 2713</pre>
=={{header|PARI/GP}}==
{{trans|Julia}}
<syntaxhighlight lang="PARI/GP">
default("parisizemax", "1024M");
\\ Define the function wilsonprimes with a default limit of 11000
wilsonprimes(limit) = {
\\ Set the default limit if not specified
my(limit = if(limit, limit, 11000));
\\ Precompute factorial values up to the limit to save time
my(facts = vector(limit, i, i!));
\\ Sign variable for adjustment in the formula
my(sgn = 1);
print(" n: Wilson primes\n--------------------");
\\ Loop over the specified range (1 to 11 in the original code)
for(n = 1, 11,
print1(Str(" ", n, ": "));
sgn = -sgn; \\ Toggle the sign
\\ Loop over all primes up to the limit
forprime(p = 2, limit,
\\ Check the Wilson prime condition modified for PARI/GP
index=1;
if(n<2,index=1,index=n-1);
if(p > n && Mod(facts[index] * facts[p - n] - sgn, p^2) == 0,
print1(Str(p, " "));
)
);
print1("\n");
);
}
\\ Execute the function with the default limit
wilsonprimes();
</syntaxhighlight>
{{out}}
<pre>
n: Wilson primes
--------------------
1: 5 13 563
2: 3 11 107 4931
3: 7
4: 10429
5: 7 47
6: 11
7: 17
8:
9: 541
10: 11 1109
11: 17 2713
</pre>
=={{header|Perl}}==
Line 1,113 ⟶ 1,242:
11 | 17 2713
</pre>
=={{header|Python}}==
<syntaxhighlight lang="python">
# wilson_prime.py by xing216
def sieve(n):
multiples = []
for i in range(2, n+1):
if i not in multiples:
yield i
for j in range(i*i, n+1, i):
multiples.append(j)
def intListToString(list):
return " ".join([str(i) for i in list])
limit = 11000
primes = list(sieve(limit))
facs = [1]
for i in range(1,limit):
facs.append(facs[-1]*i)
sign = 1
print(" n: Wilson primes")
print("—————————————————")
for n in range(1,12):
sign = -sign
wilson = []
for p in primes:
if p < n: continue
f = facs[n-1] * facs[p-n] - sign
if f % p**2 == 0: wilson.append(p)
print(f"{n:2d}: {intListToString(wilson)}")
</syntaxhighlight>
{{out}}
<pre>
n: Wilson primes
—————————————————
1: 5 13 563
2: 2 3 11 107 4931
3: 7
4: 10429
5: 5 7 47
6: 11
7: 17
8:
9: 541
10: 11 1109
11: 17 2713
</pre>
=={{header|Racket}}==
Line 1,275 ⟶ 1,449:
11 │ 17 2,713
───────┴─────────────────────────────────────────────────────────────
</pre>
=={{header|RPL}}==
{{works with|RPL|HP-49C}}
« → maxp
« { }
1 11 '''FOR''' n
{ } n
'''IF''' DUP ISPRIME? NOT '''THEN''' NEXTPRIME '''END'''
'''WHILE''' DUP maxp < '''REPEAT'''
n 1 - FACT OVER n - FACT * -1 n ^ -
'''IF''' OVER SQ MOD NOT '''THEN''' SWAP OVER + SWAP '''END'''
NEXTPRIME
'''END'''
DROP 1 →LIST +
'''NEXT'''
» » '<span style="color:blue">TASK</span>' STO
{{out}}
<pre>
1: { { 5 13 } { 2 3 11 } { 7 } { } { 5 7 } { 11 } { 17 } { } { } { 11 } { 17 } }
</pre>
Line 1,311 ⟶ 1,505:
</pre>
=={{header|Rust}}==
<syntaxhighlight lang="rust">// [dependencies]
Line 1,428 ⟶ 1,623:
{{libheader|Wren-big}}
{{libheader|Wren-fmt}}
<syntaxhighlight lang="
import "./big" for BigInt
import "./fmt" for Fmt
var limit = 11000
| |||